We model the fibre as a slender elastic beam of length \(L\)  in a viscous fluid. To account for hydrodynamic interactions, we use a local slender-body theory which is a far-field approximation of the Stokes flow due to an obstacle with a very small aspect ratio [1]}, [2]}, [3]}, allowing for shape parametrisation using the centreline position \({x}(s)\) , where \(s \in [0,L]\)  is the arc length.
